TSTP Solution File: SYO068^4.010 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SYO068^4.010 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 20:50:07 EDT 2024
% Result : Theorem 3.67s 1.80s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 33 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 190 ( 3 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 305 ( 22 ~; 20 |; 2 &; 219 @)
% ( 0 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 3 ^ 60 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(irel_type,type,
irel: $i > $i > $o ).
thf(iatom_type,type,
iatom: ( $i > $o ) > $i > $o ).
thf(iatom_def,definition,
( iatom
= ( ^ [A: $i > $o] : A ) ) ).
thf(iimplies_type,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(iimplies_def,definition,
( iimplies
= ( ^ [A: $i > $o,B: $i > $o] : ( mimplies @ ( mbox_s4 @ A ) @ ( mbox_s4 @ B ) ) ) ) ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf(ivalid_def,definition,
( ivalid
= ( '!' @ $i ) ) ).
thf(p0_type,type,
p0: $i > $o ).
thf(p1_type,type,
p1: $i > $o ).
thf(p10_type,type,
p10: $i > $o ).
thf(p2_type,type,
p2: $i > $o ).
thf(p3_type,type,
p3: $i > $o ).
thf(p4_type,type,
p4: $i > $o ).
thf(p5_type,type,
p5: $i > $o ).
thf(p6_type,type,
p6: $i > $o ).
thf(p7_type,type,
p7: $i > $o ).
thf(p8_type,type,
p8: $i > $o ).
thf(p9_type,type,
p9: $i > $o ).
thf(15,axiom,
ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11) ).
thf(69,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p10 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p10 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p9 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
thf(24,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p1 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p1 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p0 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
thf(39,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p4 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p4 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p3 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i] : ( irel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom) ).
thf(18,plain,
! [A: $i] : ( irel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i] : ( p0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( irel @ A @ B )
& ( irel @ B @ C ) )
=> ( irel @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_axiom) ).
thf(20,plain,
! [A: $i,B: $i,C: $i] :
( ( ( irel @ A @ B )
& ( irel @ B @ C ) )
=> ( irel @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
thf(29,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p2 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p2 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
thf(34,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p3 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p3 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
thf(64,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p9 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p9 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p8 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
ivalid @ ( iatom @ p10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(22,plain,
! [A: $i] : ( p10 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).
thf(44,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p5 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p5 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p4 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
thf(59,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p8 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p8 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p7 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
thf(54,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p7 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p7 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p6 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(11,axiom,
ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).
thf(49,plain,
! [A: $i] :
( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( p6 @ B ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( p6 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( p5 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(74,plain,
$false,
inference(e,[status(thm)],[69,24,39,18,16,20,29,34,64,22,44,59,54,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO068^4.010 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Jun 23 10:37:55 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.99 % [INFO] Parsing done (137ms).
% 1.26/1.00 % [INFO] Running in sequential loop mode.
% 1.82/1.20 % [INFO] eprover registered as external prover.
% 1.82/1.21 % [INFO] Scanning for conjecture ...
% 1.94/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.13/1.30 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.13/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 2.13/1.32 % [INFO] Type checking passed.
% 2.13/1.32 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.67/1.79 % External prover 'e' found a proof!
% 3.67/1.79 % [INFO] Killing All external provers ...
% 3.67/1.80 % Time passed: 1272ms (effective reasoning time: 791ms)
% 3.67/1.80 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.67/1.80 % Axioms used in derivation (13): axiom6, axiom10, axiom2, axiom11, axiom5, axiom9, trans_axiom, axiom1, axiom8, axiom4, refl_axiom, axiom7, axiom3
% 3.67/1.80 % No. of inferences in proof: 30
% 3.67/1.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1272 ms resp. 791 ms w/o parsing
% 3.72/1.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.72/1.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------